Properties of higher order stochastic cycles

Thomas Trimbur

Journal of Time Series Analysis, 2006, vol. 27, issue 1, 1-17

Abstract: Abstract. This article investigates a general class of stochastic cycles, presenting the main properties in the time and frequency domains. Harvey and Trimbur [Review of Economics and statistics (2003) Vol. 85, pp. 244–55] showed how generalized cyclical processes may be used in unobserved components models to extract smoother cycles in economic series. The stochastic cycle models allow for a flexible description of periodic behaviour in time series data. In the frequency domain, a wide variety of peaked spectral shapes, characteristic of time‐varying cyclical dynamics, is produced. The parameters have a direct interpretation, so cyclical behaviour may be studied directly; in a Bayesian approach, the researcher may implement prior views on the period in a consistent way. Extensions to multivariate models are possible.

Date: 2006
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